calculus in polynomialhow use calc. in show polynomial f=x^n+x^2-(n+2)x+n divisied of g=x^2-2x+1?

You should remember that a root of polynomial of `n-th ` order of multiplicity, cancels all the `(n-1)-th` derivative of polynomial.

Reasoning by analogy yields that if `f(x)` is divided by g(x), hence, the roots of `g(x)` are the roots of`f(x), ` moreover, if the roots of `g(x)` are roots of multiplicity 2, hence, they cancel `f(x)` and `f'(x).`

Notice that the equation of polynomial `g(x)` is the expansion of binomial `(x-1)^2` .